A parallel plate capacitor is made of two square parallel plates of area $A$ , and separated by a distance $d < < \sqrt A $ . The capacitor is connected to a battery with potential $V$ and allowed to fully charge. The battery is then disconnected. A square metal conducting slab also with area $A$ but thickness $\frac {d}{2}$ is then fully inserted between the plates, so that it is always parallel to the plates. How much work has been done on the metal slab by external agent while it is being inserted?
A parallel plate capacitor is made of two square parallel plates of area $A$ , and separated by a distance $d < < \sqrt A $ . The capacitor is connected to a battery with potential $V$ and allowed to fully charge. The battery is then disconnected. A square metal conducting slab also with area $A$ but thickness $\frac {d}{2}$ is then fully inserted between the plates, so that it is always parallel to the plates. How much work has been done on the metal slab by external agent while it is being inserted?
- A
$ + \frac{1}{4}\,\frac{{{ \in _0}A}}{d}{V^2}$
- B
$ - \frac{1}{2}\,\frac{{{ \in _0}A}}{d}{V^2}$
- C
$ + \frac{1}{2}\,\frac{{{ \in _0}A}}{d}{V^2}$
- D
$ - \frac{1}{4}\,\frac{{{ \in _0}A}}{d}{V^2}$
Similar Questions
A condenser of capacity ${C_1}$ is charged to a potential ${V_0}$. The electrostatic energy stored in it is ${U_0}$. It is connected to another uncharged condenser of capacity ${C_2}$ in parallel. The energy dissipated in the process is
A condenser of capacity ${C_1}$ is charged to a potential ${V_0}$. The electrostatic energy stored in it is ${U_0}$. It is connected to another uncharged condenser of capacity ${C_2}$ in parallel. The energy dissipated in the process is
A parallel plate capacitor after charging is kept connected to a battery and the plates are pulled apart with the help of insulating handles. Now which of the following quantities will decrease?
A parallel plate capacitor after charging is kept connected to a battery and the plates are pulled apart with the help of insulating handles. Now which of the following quantities will decrease?
A $16\ \Omega$ wire is bend to form a square loop. A $9 \mathrm{~V}$ battery with internal resistance $1\ \Omega$ is connected across one of its sides. If a $4\ \mu \mathrm{F}$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $\frac{x}{2} \ \mu \mathrm{J}$. where $x=$________.
A $16\ \Omega$ wire is bend to form a square loop. A $9 \mathrm{~V}$ battery with internal resistance $1\ \Omega$ is connected across one of its sides. If a $4\ \mu \mathrm{F}$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $\frac{x}{2} \ \mu \mathrm{J}$. where $x=$________.
- [JEE MAIN 2024]
The energy density $u$ is plotted against the distance $r$ from the centre of a spherical charge distribution on a $log$-$log$ scale. The slope of obtianed straight line is :
The energy density $u$ is plotted against the distance $r$ from the centre of a spherical charge distribution on a $log$-$log$ scale. The slope of obtianed straight line is :
A $2\,\mu F$ capacitor is charged to $100$ $volt$ and then its plates are connected by a conducting wire. The heat produced is........$J$
A $2\,\mu F$ capacitor is charged to $100$ $volt$ and then its plates are connected by a conducting wire. The heat produced is........$J$